Multimodal response characteristics of convective liquid metal sensitive layers in flexible pressure sensor | Microsystems & Nanoengineering

Microsystems & Nanoengineering volume 11, Article number: 55 (2025) Cite this article

1500 Accesses

Metrics details

The development of electronic skin, soft robots, and smart wearables has significantly driven advances in flexible pressure sensing technology. However, traditional multilayer solid-structure flexible pressure sensors encounter challenges at temperatures between 100 °C and 150 °C due to high-temperature modal distortion. Changes in the conductivity of the sensor’s conductive components interfere with accurate pressure measurement. In this research, a flexible pressure sensor with a convective liquid metal sensitive layer is proposed. The sensor uses a cyclic self-cooling mechanism to lower the temperature of its conductive components, reducing the impact of external high temperatures on the pressure measurement accuracy. At a 2.8 W thermal load, the flexible sensor, with liquid metal circulating at 2.0 mL/min, exhibits a sensitivity of 0.11 kPa⁻¹ within the pressure range from 0 to 12.5 kPa, and its maximum measurable pressure is 30 kPa. In addition, the resistance of the sensor is 18.5 mΩ less than that of a stationary liquid metal sensor, representing a 38.1% reduction. The sensor proposed in this research introduces a novel strategy for pressure measurement in high-temperature applications, extending the application scope to aircraft, special robots, and hydraulic oil circuits.

Flexible and stretchable sensors are increasingly gaining popularity for their capacity to adhere to irregular surfaces and detect diverse signals1,2. Notably, pressure sensors3,4 have garnered significant interest, and are considered a focal point in flexible sensor research. Flexible pressure sensing mechanisms primarily rely on capacitive5, piezoresistive6,7, piezoelectric8, triboelectric9, and the less common inductive10 principles. Among these mechanisms, piezoresistive sensing11 has been extensively applied in flexible pressure sensing, owing to its simple structure and straightforward readout circuitry12. Piezoresistive sensors typically consist of a sandwich structure with a flexible substrate, active materials, and electrodes, and are distinctly partitioned into conductive and structural components.

Polymers, such as rubber, elastomers, including polydimethylsiloxane (PDMS), silicone rubber, and polyurethane, serve as common structural elements in the construction of flexible sensors13. Conductive materials, such as metal nanowires, metal particles, carbon-based nanomaterials14, and conductive polymers, are extensively utilized as conductive elements in flexible sensors. However, issues, like brittleness and loss of conductivity, constrain their effectiveness in real-world applications15,16. Liquid metal17 has been widely used in flexible sensing applications due to its excellent electrical conductivity, exceptional deformability, outstanding biocompatibility, and its capacity to sensitively detect external pressure variations. Osman et al. proposed a liquid metal pressure sensor with adjustable sensitivity, which is used to monitor wrist pulsations18. Liu et al. reported a liquid metal sensor array, integrated with concave-convex microfluidic channels, which was used for detecting human movements and recognizing objects19. However, in the realm of high-temperature flexible electronics, thermal effects negatively impact the performance of flexible sensors, such as thermal stress, thermal expansion, and creep. This can result in a discrepancy between the sensitive layer of the solid material and substrate properties, adversely disrupting pressure measurements and possibly causing leakage problems.

Numerous studies had addressed the impact of temperature on pressure sensor signals, with typical focus on temperature compensation strategies20. For example, these methods included hardware approaches, like the use of Wheatstone bridges21, as well as software techniques employing artificial intelligence22. The hardware approach to temperature compensation often struggles with questionable reliability and narrow applicability, while the software method was challenged by high implementation costs and system complexity. Thus, a superior approach had been proposed to mitigate interference in pressure measurements, involving the development of conductive composites with temperature-independent conductivity23. Meng et al. had developed a method utilizing screen printing technology for the conformal deposition of temperature-independent, secondarily-doped poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) onto microstructured PDMS substrate surfaces24. Yin et al. had engineered a pressure sensor with an active layer, composed of thermoplastic polyurethane/carbon nanofiber (TPU/CNFs) sponges coated with graphene. The graphene coating mitigated temperature-induced resistance fluctuations, effectively eliminating the interference between temperature effects and pressure measurements25. Furthermore, Chen et al. proposed a pressure sensor utilizing porous melamine foam (MF) modified with single-walled carbon nanotubes (SWCNTs) and PEDOT:PSS. By leveraging the thermoelectric effect of PEDOT:PSS for temperature measurement and the microstructural elasticity of MF for pressure detection26. In scenarios with thermal loads, the standard approach for flexible pressure sensors is to utilize composite materials that exhibit either temperature-independent or low-temperature-dependent conductivity27. However, the development of conductive composites that can achieve either temperature-independent or low-temperature-dependent conductivity continues to be a formidable challenge. To address this, the research attempts to employ an alternative strategy for the fabrication of flexible pressure sensors suitable for thermal load scenarios. This strategy aims to stabilize the temperature of the conductive material within flexible pressure sensors, thereby mitigating fluctuations induced by thermal loads and maintaining consistent conductivity of the sensor’s conductive material under these conditions. The research presents a flexible pressure sensor, highlighted by its liquid metal convection-sensitive layer. The sensor’s structure is composed of silicone rubber, showcasing excellent deformability, and its conductive element is a gallium-based alloy (EGaIn), celebrated for its superior conductivity, exceptional deformation performance, and liquid-like fluidity. The flexible sensor features a serpentine microfluidic structure which ensures stable signal transmission throughout the deformation process. This design effectively amplifies the resistance change magnitude induced by pressure increases.

The research proposed a flexible pressure sensor with a liquid metal convection sensitive layer, employing a strategy to maintain conductivity by ensuring thermal stability of the conductive components under thermal load conditions. The sensor incorporates an open microfluidic structure, which liberates the liquid metal from the constraints of a sealed microchannel and enables it to flow freely within the channels. The liquid metal within this unique design structure serves a dual function: it acts as both a signal detection and transmission medium for the pressure sensor and also as a cooling medium within the thermal management system. The liquid metal within the sensor is designed to circulate, enabling cooled liquid metal to replace the heated liquid metal within the microfluidic channel. This mechanism effectively lowers the temperature of the liquid metal within the microchannels swiftly, ensuring minimal significant fluctuations in the liquid metal’s temperature. Thus, the cyclic self-cooling of the liquid metal with in the sensor can mitigate the effects of temperature on the liquid metal’s electrical conductivity, thereby reducing the interference of temperature with pressure measurements. The flexible sensor with an open microfluidic channel structure not only mitigate temperature interference during pressure measurement through cyclic self-cooling, but also effectively alleviate leakage issues caused by inconsistent deformation of the structure and conductive components at high temperatures. The flexible pressure sensor featuring liquid metal convection represents a groundbreaking innovation that transcends the constraints of conventional materials. It enables precise temperature regulation within a specified range, thereby effectively mitigating the adverse effects of temperature fluctuations on signal measurement stability and optimizing controllable modal coupling.

The flexible pressure sensor, featuring a liquid metal convection sensitive layer, utilizes EGaIn for its conductive component, which remains liquid at room temperature. The structural component consists of flexible silicone rubber, known for its high stretchability and deformability. The basic formula for resistance is expressed as R = ρL/s (where R is the resistance in Ω, ρ is the resistivity in Ω·m, L is the length of the conductive component in m, and s is the cross-sectional area in m²). Accordingly, the resistance value of the sensor is related to the dimensions of the microfluidic channel. Pressure is transmitted through the sensor to the internal microfluidic structure, causing it to deform and alter the shape of the liquid metal, which in turn results in changes in sensor resistance. In Fig. 1a, the embedded microfluidic flexible elastomer has a length L1 and a width a. The internal microfluidic channel measures w in width and h in height, with the elastomer’s wall thickness being z. The pressure on the upper surface of the elastomer is F, and the width of the microfluidic channel from left to right is l. Assuming that the pressure (F) generates a uniformly distributed pressure (P) on the upper surface of the flexible sensor, where P is calculated using the formula P = F/(L1a) (where P is in Pa, F is in N, L1 is in m, and a is in m). In this research, numerical simulations are conducted utilizing the COMSOL Multiphysics simulation software. Observations from the microfluidic channel deformation diagram (Fig. 1b) reveal that the channel undergoes deformation, with height deformation exceeding width deformation. This study focuses on an investigation of the microfluidic channel height deformation.

a Schematic diagram of the flexible sensor profile structure. b Simulation of microchannel deformation within the flexible sensor under pressure. c Schematic of the flexible sensor sandwich structure. d Flowchart of the flexible sensor manufacturing process. e Physical image of the flexible sensor with overall dimensions of 40 mm × 40 mm and microchannel size of 800 μm × 600 μm

Assuming that the silicone rubber elastomer is an ideal elastomer, no residual deformation will occur once the pressure is removed. In the case of small deformation, the height deformation in the microfluidic channel is divided into two parts: vertical displacement and downward bending shape variable. According to Yong-Lae Park’s research28, in conjunction with principles from fracture mechanics and contact mechanics29, micro-flow channels can be regarded as micro-cracks inside the sensor. The height of the micro crack under uniform normal stress will change, resulting in an opening displacement ∆h. According to the formula of linear elastic fracture mechanics (LEFM):

Where ∆h is the opening displacement of the microcrack (m), vp is the Poisson’s ratio of the sensor’s flexible material, w is the sensor’s microchannel width (m), ∂z is the stress exerted along the Z axis (normal stress) (Pa), and E is the elastic modulus (Pa) of the sensor’s flexible material (flexible elastomer). The microchannel size is significantly smaller than the sensor size, and its influence on the stress distribution is negligible. The contact stress near the microchannel is approximately ∂z = −P.

The cross-sectional area change value ∆S1 (m2) caused by vertical displacement in the microchannel height shape variable is estimated as:

The vertical displacement of the microchannel is proportional to the width of the microchannel, the contact stress, and the material’s Poisson’s ratio. Consequently, the cross-sectional area change caused by the vertical displacement can be increased by appropriately increasing the width of the microchannel. The downward bending quantity of the microchannel height shape variable can be simplified as that of a simply supported beam with a long width w and a uniform distributed load P. The downward bending quantity h(l) of the surface of the microchannel along the direction of the width l is obtained by using the deflection formula of a simply supported beam with a uniform distributed load P:

Where l is the width from the microchannel to the starting end (m), and EI is the bending stiffness of the surface of the microchannel (Pa·m3). The downward bending of the microchannel height shape variable leads to the change value ∆S2 (m2) of the cross-sectional area. The integral formula can be obtained as follows:

The downward bending deformation of the microchannel is proportional to both the width of the microchannel and the contact stress. Increasing the microchannel width enhances the change in cross-sectional area resulting from this bending. Consequently, the width of the microchannel is directly proportional to the change in cross-sectional area. The variation in microchannel height leads to a total change in cross-sectional area (∆S, m²) and a corresponding change in resistance (∆R, Ω):

The variation in cross-sectional area (∆S) caused by changes in the microchannel height can be considered negligible compared to the initial cross-sectional area (S). Therefore, Eq. (1.7) can be simplified accordingly.

The conductive and structural components of the sensor have been established, with the elastic modulus (E), Poisson’s ratio (νp), and bending stiffness (EI) of the structural component, as well as the resistivity (ρ) of the conductive component, remaining constant. The change in sensor resistance (∆R) is solely dependent on the dimensions of the microchannel. Specifically, ∆R is directly proportional to the uniformly distributed load (P), the width (w), and the length (L) of the microchannel, while being inversely proportional to the height (h) of the microchannel. The conductive components of the sandwich-structured sensor, as illustrated in Fig. 1c, feature a serpentine configuration. The sensor incorporates longer microchannels within a fixed-size elastomer, resulting in more pronounced resistance changes.

The microfluidic channels within the flexible sensor, due to their miniature size and superior deformability, exceed the fabrication capabilities of conventional 3D printing technologies. Therefore, this research employs a mold preparation method30. The aluminum alloy mold, with a surface roughness (Ra) of 1.5 to 3.2 μm, is crafted utilizing a CNC machining platform (Taiqun Seiki T-V856S linear guideway vertical machining center, Shenzhen, Guangdong). It offers several advantages, such as thermal stability, resistance to deformation, and uniform temperature distribution during the heat curing process, compare to molds prepared by 3D printing. The sensor structure is crafted from a fully transparent, two-component liquid silicone rubber. The A and B components are mixed in a 1:1 mass ratio, and curing reaction is achieved through cross-linking and catalytic reactions. With its high elasticity, exceptional transparency, and cost-effectiveness, cured transparent silicone rubber emerges as an optimal material for the structural components of flexible sensors.

Figure 1d illustrates the fabrication process of the flexible sensor. The rubber components A and B are blended in a 1:1 mass ratio by pouring them into a container. The surface of the metal mold is treated with a release agent to ease demolding, followed by pouring the homogeneously mixed silicone rubber into the mold and scraping it flat. Subsequently, it is subjected to a vacuum drying oven at 80 °C for a curing period of 2 h. The silicone rubber material, after demolding, is measured to be 1.5 mm in height (Supplementary Fig. S1). The liquid silicone rubber composite material, prepared following an identical procedure, is coated onto a clean glass sheet. The coated glass sheet is then allowed to stand, during which the silicone rubber self-levels. After self-leveling on the glass surface, the silicone rubber is then placed in a vacuum drying oven at 80 °C and heated for 5–7 min for semi-curing. During the semi-curing process, the duration of heating is strictly controlled. Tweezers were delicately employed to determine if the silicone rubber had reached the desired state of adhesion. The test is successful if the tweezers slightly adhered to the silicone without leaving any residue on its surface. The semi-cured microfluidic channel part is bonded to the cover plate, and then subjects to a thermal curing process in a vacuum drying oven at 80 °C for 2 h to ensure complete adhesion. After the curing process, the sensor is cut to the specified dimensions. Stainless steel syringes, with outer diameters of 0.63 mm, inner diameters of 0.39 mm, and lengths of 25 mm, are inserted into the inlet and outlet of the sensor. The connections are subsequently sealed with a transparent and flowable adhesive to prevent leakage. During the injection of liquid metal into the sensor, contact with air is inevitable, which easily triggers an oxidative response in the liquid metal. The oxidative state significantly alters the physical properties of liquid metal, such as viscosity, thermal conductivity, and electrical conductivity. Hence, it is essential to use a liquid metal alloy that exhibits inherent resistance to oxidation. C6H8O6, known for its antioxidant properties, was homogeneously mixed with the liquid metal at a specific ratio under an inert gas environment. The inherent reducing properties of C6H8O6 endow the liquid metal with antioxidant capabilities, effectively preventing oxidation during the injection process. The flexible sensor, once injected with liquid metal, is integrated into the liquid metal circulation system. Concurrently, a flexible pressure sensor with a liquid metal convection-sensitive layer is fabricated.

The sensor’s overall dimensions in this paper are 40 mm × 40 mm (length by width). There are three types of microfluidic channel sizes: 600 μm × 800 μm, 800 μm × 800 μm, and 800 μm × 600 μm (height × width). Figure 1e shows a sensor with dimensions of 800 μm × 600 μm and a height of 2.9 mm (refer to Supplementary Figs. S1, S2 for additional details).

Typically, piezoresistive sensors are designed with a closed structure to effectively prevent the escape of liquid metal. In contrast, the flexible sensor described in this paper, with a liquid metal convection-sensitive layer, incorporates an open structure to facilitate convection. This design integrates an external liquid metal circulation system to regulate the temperature of the sensor’s conductive components and to prevent leakage from inconsistent deformation. The sensor resistance is measured by voltammetry. A programmable linear power supply delivers a steady current to the liquid metal within the sensor, and an oscilloscope monitors the voltage difference between the inlet and outlet of the sensor. Stainless steel exhibits excellent electrical conductivity and demonstrates exceptional corrosion resistance against EGaIn. The electro-hydraulic coupling component of the sensor is a stainless steel needle tube, with copper wires tightly encircling the outer wall, and a liquid metal flow channel on the inner wall to optimize current conduction. The liquid metal circulation system utilizes Polytetrafluoroethylene (PTFE) piping, characterized by its exceptional resistance to EGaIn corrosion, rendering it an ideal choice for EGaIn transportation. A Luer interface tightly connects the PTFE tubing with the stainless steel needle tube, and the connection mode is simple and reliable. A peristaltic pump extrudes the pipeline to drive the fluid, acting as the power source for the liquid metal circulation system without contacting the EGaIn, and enabling quantitative and constant speed control. Figure 2a presents a schematic representation of the sensor resistance voltammetry measurement system. The programmable linear DC power supply provides a 0.1 A constant current to avoid the interference of Joule heating generated from the liquid metal within the sensor. The oscilloscope measures the voltage difference between the two ends of the sensor, and the resistance value is calculated by multiplying the voltage value by 10.

a Schematic diagram of the experimental setup for resistive voltammetry measurements of a flexible piezoresistive sensor. b Physical representation of the resistance voltammetry measurement platform for the flexible piezoresistive sensor. c Schematic illustration of liquid metal circulation for heat dissipation in the flexible sensor

Figure 2b is composed of three main components: temperature regulation, resistance measurement, and a device for generating pressure and temperature. The liquid metal circulation system, tasked with temperature regulation, consists of PTFE tubes, Luer connections, stainless steel syringes, and a peristaltic pump. The resistance measurement system is assembled from a programmable linear DC power supply and an oscilloscope. And a device for generating pressure and temperature encompasses a force generator, a flexible heating plate, a silicone pad, and a regulated DC power supply. The DC regulated power supply provides a constant power input to the flexible heating plate, facilitating the simulation of high-temperature environments. The force generator exerts a certain pressure on the upper surface of the sensor, and the peristaltic pump ensures efficient cooling of the liquid metal. Additionally, the programmable linear power supply, in tandem with the oscilloscope, utilizes voltammetry to precisely measure fluctuations in sensor resistance. In Fig. 2c, the inlet and outlet of the sensor, with open architectures, enable the liquid metal circulation system to efficiently reduce the temperature of the conductive elements within the microfluidic channel. This design effectively dissipates heat to the surroundings, reducing the interference of high temperature on pressure measurement.

The piezoresistive sensing mechanism detects the applied pressure magnitude by monitoring the deformation of the conductive material. When the upper surface of the sensor is subjected to mechanical stresses, including pressure and impact, as illustrated in Fig. 3a, the liquid metal within the microfluidic channel undergoes a morphological change. This alteration results in a commensurate change in sensor resistance. Surface pressure causes deformation in the microfluidic channel, which in turn changes the flow resistance within the channel. Consequently, this deformation also affects the sensor inlet pressure and outlet flow rate. In this experiment, the Reynolds number for EGaIn ranges from 1.5 to 12, substantially below the critical threshold of 2000, and the flow state is laminar. In this study, the COMSOL Multiphysics software is utilized to numerically simulate the flow velocity distribution and the deformation within the microfluidic channel under pressure. The inlet pressure is specified at 1 kPa, and the uniform pressure exerted on the upper surface is set to 9 kPa. A cross-sectional analysis of the sensor is selected, with the flow velocity distribution and deformation depicted in Fig. 3b, c, respectively (800 μm × 800 μm microfluidic flexible sensor is shown in Supplementary Fig. S3). Significant deformation occurs on both sides of the sensor under pressure. Owing to the high surface energy of EGaIn, the flow velocity at the microfluidic channel wall is lower than that in the center region of the pipe, reaching its maximum near the centerline. Within microfluidic channels, sections with a width of 600 µm are longer than those with a width of 800 µm. Under the same conditions of cross-sectional area, inlet pressure, and pressurization, microfluidic channels with a narrower width exhibit higher flow resistance, leading to commensurately lower flow velocities. The length of the microfluidic channel has a significant impact on flow velocity. Pressure is applied at the sensor inlet, and the outlet flow rate can be derived from Poiseuille’s law for rectangular channels:

where Rflow is the flow resistance of the rectangular pipe (Pa·s·m−3), ∆P (Pa) is the pressure drop between the inlet and outlet of the flexible sensor, μ (Pa·s) is the viscosity of the fluid, w (m) is the width of the microchannel, h (m) is the height of the microchannel, L (m) is the length of the microchannel, and Q (m3/s) is the outlet flow rate of the microchannel. The pressure drop (ΔP) signifies the pressure differential between the inlet and outlet of the sensor. Assuming the outlet pressure to be 0, the pressure drop (ΔP) is therefore equal to the inlet pressure. Figure 3d demonstrates the linear relationship between inlet pressure and outlet flow rate, illustrating that the microfluidic channels with smaller widths, having the same cross-section, lead to a reduced outlet flow rate. Within the same microfluidic channel width, an increment in the microchannel height leads to an increased outlet flow. Figure 3e reveals the variation of outlet flow rate for different pressure conditions on the upper surface. Apparently, with the increase in upper surface pressure, there is a downward tendency in the outlet flow, yet the overall fluctuation is not significant. This figure also demonstrates that for microchannels with the same cross-sectional area, a narrower width corresponds to a lower initial flow rate, and the magnitude of flow rate fluctuations during deformation is correspondingly smaller. For sensors with identical specifications, a high inlet pressure is associated with a high outlet flow rate, and results in a more pronounced flow rate reduction during deformation. Among the flexible sensors of different sizes, as illustrated in Fig. 3f, the sensor with dimensions of 800 μm × 800 μm exhibits the lowest flow resistance, followed by the one with dimensions of 800 μm × 600 μm. In contrast, the sensor with dimensions of 600 μm × 800 μm has the highest flow resistance. The sensor’s flow resistance is inversely proportional to both the width and the cross-sectional area of the microfluidic channel. As the pressure exerted on the upper surface increases, all the flow resistance, as shown in Fig. 3f, tend to increase. Significantly, with the constant pressure at the sensor inlet, the changes in the upper surface pressure exert only a minor effect on the flow resistance of microfluidic channels. In subsequent studies, the peristaltic pump maintained a steady output despite variations in the upper surface pressure, ensuring a consistent flow rate at the sensor outlet. Current high-performance pump systems are capable of effectively managing flow resistance, ensuring a stable flow rate over extended periods.

a Schematic representation of pressure detection using the piezoresistive mechanism. b Simulation of pressurized deformation in a microfluidic channel with dimensions of 800 µm × 600 µm. c Simulation of pressurized deformation in a microfluidic channel with dimensions of 600 µm × 800 µm. d Graph illustrating the relationship between sensor inlet pressure and outlet flow. e Correlation between the pressure applied to the upper surface of the sensor and the outlet flow. f Relationship between the pressure on the upper surface of the sensor and the flow resistance of the microfluidic channel

For temperature regulation, as depicted in Fig. 4a, a resistive heating plate, with thermal insulation on the underside, is attached to a silicone sheet. The heat emitted by the heating plate is primarily used to warm the flexible sensor. With thermal insulation on the underside, the heating plate minimizes heat loss to the surrounding environment and reduces absorption by the silicone sheet. The flexible sensor, placed on top of the heating plate, is connected to an external liquid metal circulation system via a Luer interface. The input power of the heating plate is adjusted to simulate various high-temperature scenarios. Detecting the temperature of the liquid metal within the microfluidic channel of the sensor is challenging. In previous research, Liu et al. measured the inlet and outlet temperatures of a liquid metal-based LED heat dissipation device, and characterized the average temperature of the inlet and outlet as the mean liquid metal temperature within the device31. The electro-hydraulic coupling part of the flexible sensor, made of stainless steel, exhibits excellent thermal conductivity. Thermocouple temperature sensors are attached to the stainless steel needle tubes at both the inlet and outlet of the sensor. These sensors measure the temperature at the needle tubes, estimating the temperatures of liquid metal within the inlet and outlet of the sensor. Thus, the average temperature of the liquid metal inside the sensor is estimated from the mean temperatures of syringe at the sensor’s inlet and outlet. The temperature variation of various sensor specifications at a room temperature of 26 °C, under a thermal load of 2.8 W, and with various liquid metal input flow rates is illustrated in Fig. 4b. The heating plate, with an input power of 2.8 W, can produce high temperatures ranging from 120 °C to 150 °C. As the liquid metal flow rate increases, there is a corresponding obvious decrease in the average temperature of the liquid metal. Among sensors with identical input flow rates, the sensor with dimensions of 600 μm × 800 μm exhibited the most pronounced temperature difference of the liquid metal inside, whereas the sensor with dimensions of 800 μm × 800 μm experiences the least temperature drop. With identical input flow rates and cross-sectional areas, a narrower microchannel width correlates with a lower average temperature at both the sensor’s inlet and outlet. With the identical input flow rates and microfluidic channel width, a larger microfluidic channel size perpendicular to the heater correlates with a higher average temperature at the sensor’s inlet and outlet. The average temperature at the sensor’s inlet and outlet, under the same liquid metal input flow conditions, is inversely proportional to the width of the microfluidic channel and directly proportional to its cross-sectional area.

a Schematic of the flexible sensor’s temperature regulation system. b The average temperatures at two ports of three flexible sensors across varying microchannel sizes and flow rates. c Time-dependent graph of the average temperature for a flexible sensor with a microchannel size of 800 μm × 600 μm across various flow rates. d Temperature variations at the outlet of an 800 μm × 600 μm microfluidic channel flexible sensor, subjected to injections of gallium-based liquid metal at diverse flow rates. e Temperature variations at the outlet for sensors with microchannel dimensions of 800 μm × 600 μm and 600;μm × 800 μm, measured at flow rates of 1.5 mL/min and 2.0 mL/min for gallium-based liquid metal injections. f Outlet temperatures for two microfluidic channel configurations (800 μm × 600 μm and 800 μm × 800 μm) at 1.5 mL/min and 2.0 mL/min flow rates, with varying volumes of gallium-based liquid metal. g Average temperatures at both ends of a flexible sensor with a microchannel size of 800 μm × 600 μm, depicted as a function of flow rate variability over time. h Average temperatures at the inlet and outlet of a flexible sensor (microchannel: 800 μm × 600 μm) at a constant flow rate of 2.0 mL/min with variable power. i Periodic temperature variations of a flexible sensor with a microchannel size of 800 μm × 600 μm, recorded at a flow rate of 2.0 mL/min

As an example, consider a flexible sensor with dimensions of 800 μm × 600 μm. Figure 4c illustrates the temperature variation of this sensor over the first 5.5 min at various flow rates. The heating plate, functioning at an input power of 2.8 W, consistently heats the sensor and maintains its temperature at a stable level. Following 1 min, as the liquid metal starts to circulate, significant temperature fluctuations are observed at the sensor’s inlet and outlet, characterized by pronounced troughs and peaks. The temperature changes exhibit distinct valleys and peaks, but overall, they show a trend of decreasing temperatures. In the context of the sensor’s temperature fluctuations, the smaller the liquid metal input flow rate, the longer the crest exists, indicating a direct relationship between flow rate and the duration of temperature peaks. As a result of the warming by the heating plate, the temperature of the internal liquid metal is marginally elevated compared to the temperatures measured at the sensor’s inlet and outlet. During the circulation of liquid metal, the temperature at the inlet decreases, while the temperature at the outlet rises as the discharge of the internal high-temperature liquid metal. Consequently, this leads to an initial drop followed by a subsequent rise in the average temperature at the sensor’s inlet and outlet. An increased liquid metal input flow rate reduces the discharge time for the internal high-temperature liquid metal, consequently shortening the duration of peak temperatures. Hence, the fluctuation in average temperature at the sensor’s inlet and outlet is predominantly influenced by the temperature changes occurring at the outlet. As illustrated in Fig. 4d, a plot of injection volume versus outlet temperature under varying liquid metal input flow rates clearly shows that the injection volume differs little at the points where outlet temperature fluctuations occur, regardless of the flow rate. As the volume of liquid metal injected increases, the outlet temperature fluctuates, initial increasing and then decreasing, a trend that is consistent with the observations in Fig. 4c. Since the initial temperatures of sensors with different specifications vary, direct comparison is challenging. There is a meaningful comparison by taking into account the differences in their initial temperatures. To simplify this comparison, Fig. 4e, f depicts the correlation between injection volume and the temperature differential at the outlet under varying liquid metal input flows. It is clear that, with identical cross-sectional area of the microfluidic channel, a narrower channel width results in more significant decreases in outlet temperature, as shown in Fig. 4e. Figure 4f demonstrates that, for the same channel width, a large cross-sectional area of the microfluidic channel is associated with a less pronounced temperature reduction.

To further demonstrate the temperature control capability of the flexible sensor, Fig. 4g illustrates the temperature variations at the inlet and outlet of the 800 μm × 600 μm sensor across a range of liquid metal input flow rates. After the liquid metal at rest reaches a stable temperature and is further heated for 1 minute, it is circulated at a flow rate of 0.5 mL/min. The flow rate is adjusted after 4 min, and the liquid metal circulation was stopped 4 min later. During the entire period, the heating plate continuously supplies heat to the sensor at a power of 2.8 W. The average temperature of the sensor is effectively lowered by the liquid metal circulation, and a higher flow rate leads to a more significant temperature reduction, as demonstrated in Fig. 4g. Sensors in high-temperature scenarios inevitably encounter thermal shock, necessitating a certain level of thermal shock resistance. Once the liquid metal at rest reaches a stable temperature and continues to be heated for an additional minute, the liquid metal begins to circulate at a flow rate of 2.0 mL/min. After 4 min, the power of the heating plate is increased from 2.8 W to 6 W, simulating the thermal shock that the sensor would experience in high-temperature environments. Figure 4h illustrates the average temperature fluctuations of the sensors throughout the process. These fluctuations, particularly during thermal shock tests, demonstrate that liquid metal circulation significantly reduces the average temperature. Moreover, the temperature rise due to thermal shock is markedly lower in circulating liquid metal compared to when it is static, underscoring the effectiveness of the temperature control mechanism. Cyclic stability, a crucial performance metric for sensors, is demonstrated in Fig. 4i, which shows the average temperature cycle variation of the sensor. The sensor, with liquid metal at rest, is heated to a stable temperature and this heating is maintained for 6 min. It is then followed by circulating the liquid metal at a flow rate of 2.0 mL/min for 3 min. After the circulation stops, the liquid metal in the sensor is heated for another 6 min to complete one cycle of the process. The sensor cooling cycle exhibits excellent stability, as shown in Fig. 4i. The liquid metal circulation system reduces the sensor temperature several times. The flexible sensor with a liquid metal convection-sensitive layer proposed in this study can significantly reduce the average temperature, exhibits robust thermal shock resistance, and maintains excellent cycle stability, making it ideal for high-temperature scenarios.

In this study, a stainless steel syringe is utilized to deliver current inside the sensor. The exterior of the stainless steel needle tube is wrapped with a copper wire, and the interior wall serves as a channel for liquid metal flow. In this setup, undesirable contact interfaces exist between the liquid metal and the inner wall of the stainless steel syringe, as well as between the outer wall of the syringe and the external copper wire. The resistances at these interfaces, along with the wire connection resistance, are summarized as wire contact resistance, stainless steel tube resistance, and solid-liquid contact resistance, all of which are connected in series. The high viscosity of the liquid metal impedes achieving an optimal contact state on the inner wall of the stainless steel needle tube, resulting in fluctuating contact resistance at the electrode interface. The variation in contact resistance of liquid metal flowing inside the wall of a stainless steel syringe (with an inner diameter of 0.39 mm, a wall thickness of 1.2 mm, and a length of 4 mm) is shown in Fig. 5a. The stochastic fluctuations in solid-liquid contact resistance and stainless steel needle tube resistance show a decreasing trend with increasing flow rate, but the changes were not significant. The copper wire, coiling around the exterior of the stainless steel syringe for current transmission, creates an uneven contact interface with the outer wall, reducing the actual contact surface area. Achieving an ideal interface between the copper wire and the stainless steel needle tube’s outer wall is challenging. Moreover, achieving complete filling of the liquid metal in the inner wall is also difficult. These irregular interfaces result in dynamic changes in the overall contact resistance at the electrode. The resistance variation of a stainless steel syringe (with 0.39 mm in inner diameter, 1.2 mm in wall thickness, and 4 mm in length) is depicted in Fig. 5b when wrapped with a copper wire and filled with liquid metal. The resistance at the external copper wire electrode is significantly higher than that without the external copper wire electrode. Moreover, it is worth noting that a higher liquid metal flow rate is associated with a lower resistance, which is consistent with the variations observed in Fig. 5a. As the flow of liquid metal increases, the resistance fluctuations become less significant. To minimize the effect of electrode resistance fluctuations on the sensor’s future resistance measurements, it is recommended to select a higher input flow rate.

a Input flow rates of 1.0 mL/min and 2.0 mL/min without resistance at the electrode of the external copper wire. b Waveform diagram of the total resistance at the external copper wire electrode for input flow rates of 1.0 mL/min and 2.0 mL/min. c Resistance characteristics of the flexible sensor at various flow rates. d Resistance waveform of the sensor with dimensions 800 μm × 600 μm at input flow rates of 1.0 mL/min and 2.0 mL/min

The flexible sensor with a liquid metal convection-sensitive layer operates on a piezoresistive sensing mechanism, which measures the applied pressure by altering its own resistance through the deformation of the liquid metal. This sensor mitigates the influence of temperature on pressure measurement via the liquid metal cycle, but the high surface energy of the liquid metal induces fluctuations in the sensor’s resistance at varying flow rates. Figure 5c illustrates the resistance of different sensor specifications under varying flow rates. As the flow gradually rate increases, the resistance exhibits a decreasing trend, indicating that the sensor resistance is inversely proportional to the input flow rate. Among the sensors, the 600 μm × 800 μm sensor features the longest microfluidic channel length and the smallest cross-sectional area, resulting in the largest resistance. The resistance of the 800 μm × 600 μm sensor ranks second, and the 800 μm × 800 μm sensor displays the lowest resistance. Additionally, the resistance fluctuations in sensors with higher resistance are more pronounced. Taking the 800 µm × 600 µm sensor as an example, Fig. 5d depicts the resistance fluctuations of the sensor at flow rates of 1.0 mL/min and 2.0 mL/min. Although the sensor resistance is in a fluctuating state, the overall fluctuation remains small and within a stable range. Sensors with smaller liquid metal input flow rates exhibit more pronounced resistance fluctuations. The resistance of the sensor at an input flow rate of 2.0 mL/min is approximately 845 mΩ, and the resistance of the sensor with an input flow rate of 1.0 mL/min is about 903 mΩ, with the 2.0 mL/min sensor having a 58 mΩ lower resistance than the 1.0 mL/min sensor. Sensor resistance decreases with higher liquid metal input flow rates. Therefore, for subsequent pressure measurements, 2.0 mL/min is selected as the input flow rate for the flexible sensor.

The flexible pressure sensor, featuring a liquid metal convection-sensitive layer, is designed for high-temperature applications and mitigates the interference of high temperature on sensor resistance. The sensor, measuring 800 μm × 600 μm, is subjected to varying heating powers to simulate different high-temperature conditions. Figure 6a shows the resistance characteristics of the sensor, measuring 800 μm × 600 μm, at varying heating powers. The resistance of the flexible sensor in high-temperature scenarios rises as the heating power increases. Specifically, at a 2.8 W thermal load, the sensor resistance increases by 48.5 mΩ, resulting in a 5% increase. This indicates that the sensor resistance in high-temperature conditions is subject to certain interference, necessitating that the sensor possess a degree of resistance to thermal interference. Figure 6b shows the difference in sensor resistance for various thermal loads, comparing liquid metal flowing at 2.0 mL/min with room temperature and liquid metal at rest. In high-temperature scenarios, the self-resistance of the sensor at a liquid metal input flow rate of 2.0 mL/min shows an upward trend, although the resistance difference is minimal. In addition, as the thermal load increases, the resistance difference between the sensor with a flow rate of 2.0 mL/min and at rest gradually increases. At 2.8 W thermal load, the sensor resistance for the 2.0 mL/min input flow rate increases by only 30mΩ, which is 18.5 mΩ lower than that of the sensor of the liquid metal at rest, reflecting a decrease of 38.1%. Rapid discharge of the internal high-temperature liquid metal significantly reduces the average sensor temperature, helping to maintain the liquid metal’s temperature within the sensor at a stable level. Flexible pressure sensors with liquid metal convection-sensitive layers reduce temperature interference with sensor resistance.

a Resistance difference of the 800 μm × 600 μm flexible sensor under various heating powers. b The difference in sensor resistance for various thermal loads, comparing liquid metal flowing at 2.0 mL/min with room temperature and liquid metal at rest. c Relationship between upper surface pressure and resistance of the 800 μm × 600 μm flexible sensor at 2.8 W heating power and room temperature. d External pressure and resistance characteristics of the 800 μm × 600 μm flexible sensor with a liquid metal input flow of 2.0 mL/min at room temperature and 2.8 W heating power. e Comparison of external pressure and resistance differences of the 800 μm × 600 μm flexible sensor with input flow rates of 2.0 mL/min and 0 mL/min at 2.8 W. f Cyclic loading resistance of the flexible sensor at 2.8 W heating power with a 2.0 mL/min liquid metal input flow rate of 800 μm × 600 μm

In the stationary state of the liquid metal circulation system, with pressure applied to the sensor’s upper surface, Fig. 6c illustrates the resistance variation under different heating scenarios at room temperature and 2.8 W. Notably, the amplitude of resistance change at room temperature is significantly smaller than that at high temperatures. The decrease in the liquid metal’s conductivity and the thermal deformation of the microfluidic channel in response to applied pressure result in larger resistance changes. However, this also introduces increased fluctuations in resistance measurements and larger measurement errors. At room temperature, applying 4 N to the sensor’s upper surface results in a uniform pressure of 2.5 kPa and a resistance change of 25–30 mΩ. When a 4 N force is applied to the center area of the sensor’s upper surface using a 15 mm diameter force generator, the local pressure reaches 22.6 kPa, causing the resistance to change by 81 mΩ. This change is 2.7–3.2 times greater than the resistance change observed under uniform pressure, indicating a dramatic increase in resistance. With the same applied force at the sensor, the strong local pressure state leads to noticeable resistance changes, indicating excellent pressure response performance. Placed under a 2.8 W thermal load with a uniform force on its upper surface, the sensor’s resistance variation with applied pressure is depicted in Fig. 6d for both the liquid metal at rest and during a 2.0 mL/min flow condition. The resistance of the sensor with a 2.0 mL/min input flow rate is significantly reduced, exhibiting a small range of resistance fluctuation and high measurement accuracy, but the slope is low, resulting in less obvious pressure response performance. Liquid metal flows in the microfluidic channel in the presence of hydrostatic pressure, there is some resistance to the pressure exerted on the upper surface, thus rendering the pressure response less apparent. With a liquid metal input flow rate of 2.0 mL/min and a uniform load applied to the upper surface, Fig. 6e displays the change in sensor resistance with pressure at room temperature and 2.8 W thermal load. The linear fit of sensor resistance changes in the room temperature scenario is excellent, but the resistance change is minimal, and the pressure response is not pronounced. In contrast, high-temperature scenarios show significant variation in sensor resistance, with an obvious pressure response. Figure 6f displays the cycle diagram of a uniform 10 kPa load applied to the upper surface of the sensor, under a 2.8 W thermal load and a 2.0 mL/min input flow rate. The load is applied at 11 s, removed at 21 s, completing one cycle of 35 s. It is clear that the resistance change caused by a 10 kPa load is significant, showing distinct loading resistance changes. Although there is some fluctuation in the resistance due to loading, it remains stable within a defined range. This demonstrates a pronounced pressure response and excellent cyclic stability.

Sensor sensitivity is a crucial indicator for evaluating sensor performance, characterizing the sensor element’s response to external changes, and affecting the sensor’s measurement accuracy and reliability The sensitivity of the sensor is defined as the ratio of the output signal to the input signal under stable operating conditions, determined by the slope of the ∆R/R curve. The following formula represents the sensitivity calculation:

where δ is a mathematical symbol that represents a change in a variable, P is the pressure applied to the upper surface of the sensor in kPa, ∆R is the resistance change value in Ω, R is the initial resistance value in Ω, S is the sensitivity of the device in kPa−1. As shown in Fig. 7a, b, the stationary liquid metal sensor’s sensitivity is 0.30 kPa⁻¹ at room temperature and increases to 0.65 kPa⁻¹ at 2.8 W heating power, respectively. The pressure response performance is excellent. High-temperature scenarios cause changes in the conductivity of the sensor’s conductive components, resulting in evident pressure-induced changes in resistance, and the sensor exhibits high sensitivity and a better response to pressure. However, with high-temperature scenarios, the fluctuations of sensor’s resistance are significant, and the resistance change varies across different temperature scenarios, introducing significant errors in pressure measurement. Figure 7c, d illustrates the sensitivity of the sensor with a liquid metal input flow rate of 2.0 mL/min at room temperature and 2.8 W thermal load. The sensitivities of the sensor are 0.08 kPa−1 and 0.11 kPa−1 for the room temperature scenario and 2.8 W thermal load, respectively. The sensitivity of the sensor with a 2.0 mL/min input flow rate is significantly lower than that of the liquid metal at rest. Due to the presence of hydrostatic pressure in the sensor of the liquid metal cycle, it resists uniform load applied to the upper surface and the actual applied load is lower than that of the liquid metal at rest, resulting in a slightly lower performance in response to pressure and a slightly lower sensitivity of the sensor. However, the sensor with a 2.0 mL/min input flow rate exhibits an excellent linear fit for resistance changes in both normal temperature and high-temperature scenarios, ensuring accurate pressure measurements. Relative to the sensors listed in Table 1, the sensors in this study demonstrate superior sensitivity and an enhanced pressure response.

a Sensitivity diagram of the sensor in the liquid metal stationary state at normal temperature. b Sensitivity diagram of the sensor in the liquid metal stationary state at 2.8 W heating power. c Sensitivity diagram of the sensor at a 2.0 mL/min input flow rate in the room temperature scenario. d Sensitivity diagram of the sensor at a 2.0 mL/min input flow rate under 2.8 W heating power. e The frequency response ratio at 8 kPa for a flexible pressure sensor. f The response time of the flexible sensor at a pressure of 8 kPa

This research describes the sensor sensitivity under four different scenarios. Among them, under the condition where the liquid metal inside the sensor is stationary, from the room temperature scenario to the 2.8 W thermal load scenario, the sensitivity nearly increased by 116.7%. In contrast, when the liquid metal is in motion, sensitivity increased by only 37.5% under the same temperature change conditions. The liquid metal circulation system of the sensor can significantly reduce the increase in sensor sensitivity across different temperature scenarios. However, the sensitivity of flexible pressure sensors with a liquid metal convection-sensitive layer still exhibits some drift under different temperature conditions. In our forthcoming research, we intend to collect data from the sensors across a spectrum of temperatures and train a convolutional neural network (CNN) to model the intricate relationship between temperature and sensor sensitivity. This model will enable us to predict and compensate for performance drifts induced by temperature fluctuations, enhancing the stability and reliability of our sensors.

Frequency response is a key measure of the dynamic response of a pressure sensor. The frequency response of a pressure sensor, often referred to as bandwidth, dictates the measurable frequency range of the applied pressure. The pressure response frequency of a pressure sensor is associated with its geometric and structural properties. Experimentally, the resistance of the flexible sensor at various frequencies under an 8 kPa pressure was measured, and the frequency response ratio of the pressure sensor to a constant pressure was derived, as illustrated in Fig. 7e. From the graph, it is clear that 50% corresponds to a frequency of about 3 Hz, and 70% corresponds to a frequency of about 1.75 Hz. Additionally, there is always some delay in the sensor’s response. Response time, which also measures the dynamic response of the pressure sensor, is the duration from when the sensor detects a pressure change to when it outputs the corresponding electrical signal. The experimental measurement of the flexible sensor’s response time at 8 kPa pressure is depicted in Fig. 7f, indicating a rise time of 0.64 s and a fall time of 0.54 s, which delineates the sensor’s dynamic response characteristics.

Pressure sensors are capable of transducing pressure variations into electrical signals, a process that is frequently marred by the presence of various forms of noise. The predominant sources of noise in these sensors are thermal noise and flicker noise. This noise can obscure or distort the sensor’s actual output signal, leading to inaccuracies in the measurement outcomes. The signal-to-noise ratio (SNR) of a pressure sensor is a critical performance metric, defined as the ratio of the power of the sensor’s output signal to that of the noise power. An elevated signal-to-noise ratio indicates superior signal quality from the sensor output and implies a diminished impact of noise on the signal. In this research, the initial resistance of the flexible pressure sensor, which features a liquid metal convection-sensitive layer, is measured at 965.1 mΩ. The sensor’s terminals are connected to a constant current source, and the voltage across the sensor is analyzed using discrete Fourier transform to derive the power spectral density (PSD) map. Based on the PSD plot, the useful power and noise power are integrated. The signal-to-noise ratio is calculated using the following formulas:

where Pnoise is the noise signal power in W, Ptotal is the total power in W, Psignal is the useful signal power in W, SNR is the signal-to-noise ratio in dB. The signal-to-noise ratio of the pressure sensor, as determined by the discrete Fourier transform analysis, is 43.5 dB. This high SNR indicates that the sensor designed in this study can deliver a clear signal with lower noise interference.

Under a 2.8 W heating scenario and with a 2.0 mL/min liquid metal input flow rate for the flexible sensor, Fig. 8a illustrates the changes in sensor resistance during the loading and unloading process. As the sensor is subjected to pressure, its resistance increases gradually. Over a pressure gradient ranging from 0 to 12.5 kPa, the sensor exhibits a rapid and stable response to variations in loading and unloading pressure. The flexible sensor is designed to conform to irregular surfaces, making it suitable for pressure measurements in pipelines. The high hydraulic test bench can simulate various liquids under different temperature conditions, which may affect the sensor’s pressure measurements. The flexible sensor proposed in this study effectively reduces the influence of temperature on pressure readings and is capable of measuring line pressures of supply and return fluids across a range of temperatures. Figure 8b depicts the flexible sensor affixed to a high hydraulic simulation platform. The polyurethane copper-plated telescopic steel wire vacuum collection hose, primarily composed of polyurethane (PU) and copper-plated steel wire, is utilized for ventilation and exhaust, capable of expelling steam and welding fumes, as well as conveying oil and air in food processing and pneumatic tools. A flexible sensor with a highly sensitive liquid metal layer is affixed to the inner wall of the pipeline, ensuring accurate pressure measurements and the safety of pipeline transportation. Figure 8c presents a physical diagram of the flexible sensor mounted within the polyurethane copper-plated telescopic steel wire dust suction pipe, ensuring that the temperature of the transported material does not interfere with pressure measurement. A flexible sensor mounted on a hydraulic platform receives a 2.0 mL/min stream of metallic fluid under a uniform load and with a constant input pressure of 50 mV. Figure 8d illustrates the relationship between the current of the flexible sensor and the applied pressure, which decreases as the pressure increases. With a constant input voltage, the output current decreases with higher applied pressure.

a Resistance change diagram of the flexible sensor under loading and unloading conditions of 0 to 12.5 kPa. b Physical diagram of the flexible sensor affixed to the oil supply and return pipelines on the high hydraulic experimental platform. c Physical drawing of the flexible sensor mounted on the polyurethane copper-plated telescopic steel wire suction pipe. d Diagram of resistance versus pressure of a flexible sensor pasted on a hydraulic platform

The flexible pressure sensor developed in this research features a sensitive layer utilizing a liquid metal convection design. The calibration and thermal experiments for this sensor are predominantly executed under planar conditions. However, when the sensor is adhered to the pipeline, its performance may be compromised as a result of alterations in the microfluidic channel geometry. Therefore, in our future research, we intend to employ simulation software to simulate the performance of the sensor on pipes of varying diameters and conduct a comparative analysis with the baseline performance data obtained under flat surface conditions. We will consider pipe diameter, thermal load, and pressure as independent variables, and the variation in sensor resistance among other performance metrics as the dependent variable. We will then utilize a linear regression model to establish the relationship between these independent and dependent variables. The aim is to develop a mathematical model capable of predicting sensor performance across various pipeline scenarios.

The flexible pressure sensor, featuring a convection liquid metal sensitive layer, benefits from a simple manufacturing process, a straightforward structure, and an easy working principle, making it suitable for large-scale production. They also feature stretchability, conformity to test surfaces, and a rapid response to pressure. These sensors exhibit accurate measurement accuracy, excellent repeatability, and stable cyclic performance, making them ideal for reliable data collection. The sensor proposed in this research effectively reduces the influence of temperature on its resistance and pressure measurements, minimizing temperature interference in high-temperature scenarios. This sensor has a wide range of applications in aircraft, special robots, and hydraulic oil circuits. Furthermore, it offers new insights for the research and application of high-temperature flexible sensing technology.

We have introduced a flexible pressure sensor with a liquid metal convection-sensitive layer that requires an external pumping system for the liquid metal. The system’s bulkiness, largely due to the pump’s size, poses challenges in integrating it into thermal load environments. To resolve this challenge, we plan to employ a more compact pump system in our future research to actuate the liquid metal within the sensor. Currently, within the microfluidics domain, piezoelectric pumps32 have become integral to precise fluid control due to their compact dimensions, high performance, and accurate flow regulation capabilities. They are extensively utilized in portable diagnostic devices and lab settings. In our forthcoming research, we intend to replace the bulky peristaltic pumps with piezoelectric pumps as the driving force for the liquid metal circulation system. This substitution is expected to markedly decrease the system’s bulk, enhancing the flexibility of the sensor system and facilitating its integration into thermal load environments. The placement of the external pump directly influences the piping layout, which in turn affects the heat transfer efficiency and the overall sizing of the sensor system. The shape and layout of the pipes will be specifically tailored to match the application scenarios of the sensors. Flexible pipes will be fabricated using 3D printing technology, which not only ensures excellent flexibility but also offers great freedom in designing the pipe paths. Furthermore, the flexible pressure sensor with a liquid metal convection-sensitive layer, as proposed in this research, faces size limitations, which complicates the arrangement in arrays and limits its application scope. Therefore, in our future research, we will employ micro-nano 3D printing, electrospinning, and soft lithography to fabricate microchannels ranging from 50 to 200 μm in size, thereby constraining the overall sensor dimensions to a compact 4–6 mm. This design will enable the sensor to be distributed in arrays, facilitating contact-based mechanical imaging for robots.

Hu, X. D. et al. High-resolution, high-speed and low-cost flexible tactile sensor array system. Measurement 241, 115630 (2024).

Google Scholar

Wang, L. Q., Zhu, R. & Li, G. Z. Temperature and strain compensation for flexible sensors based on thermosensation. ACS Appl. Mater. Interfaces 12, 1953–1961 (2019).

MATH Google Scholar

Li, L., Sun, Y. Q. & Sun, W. Design of Flexible Pressure Sensor Applied to Mechanical Gripper. IEEE Sens. J. 22, 15793–15801 (2022).

MATH Google Scholar

Bijender & Kumar, A. Recent progress in the fabrication and applications of flexible capacitive and resistive pressure sensors. Sens. Actuator A Phys. 334, 113770 (2022).

MATH Google Scholar

Gong, W. Z., Lian, J. H. & Zhu, Y. L. Capacitive flexible haptic sensor based on micro-cylindrical structure dielectric layer and its decoupling study. Measurement 223, 113785 (2023).

MATH Google Scholar

Yi, Y., Liu, E. Z. & Deng, H. Porous Flexible Piezoresistive Sensor Using Liquid Metal for Low Pressure Detection. Sens. Actuator A Phys. 375, 115536 (2024).

MATH Google Scholar

Park, Y. L., Chen, B. R. & Wood, R. J. Design and Fabrication of Soft Artificial Skin Using Embedded Microchannels and Liquid Conductors. IEEE Sens. J. 12, 2711–2718 (2012).

MATH Google Scholar

Tian, H. Y. et al. Serpent-inspired multimodal flexible sensor for multi-signal measurement based on PVDF-TrFE/Fe3O4 nanofibers. Measurement 236, 115074 (2024).

MATH Google Scholar

Qu, X. C. et al. Fingerprint-shaped triboelectric tactile sensor. Nano Energy 98, 107324 (2022).

Google Scholar

Hamaguchi, S. et al. Soft inductive tactile sensor using flow-channel enclosing liquid metal. IEEE Robot. Autom. Lett. 5, 4028–4034 (2020).

MATH Google Scholar

Li, Y. X. et al. A Flexible Capacitive Pressure Sensor with Adjustable Detection Range Based on the Inflatable Dielectric Layer for Human-Computer Interaction. ACS Appl. Mater. Interfaces 16, 40250–40262 (2024).

Google Scholar

Vertuccio, L. et al. Piezoresistive properties of resin reinforced with carbon nanotubes for health-monitoring of aircraft primary structures. Compos. B. Eng. 107, 192–202 (2016).

Google Scholar

Duan, L. Y., D’hooge, D. R. & Cardon, L. Recent progress on flexible and stretchable piezoresistive strain sensors: From design to application. Prog. Mater. Sci. 114, 100617 (2020).

Google Scholar

Chen, D. P. et al. Structure and function design of carbon nanotube-based flexible strain sensors and their application. Measurement 225, 113992 (2023).

Google Scholar

Nag-Chowdhury, S. et al. Non-intrusive health monitoring of infused composites with embedded carbon quantum piezo-resistive sensors. Compos Sci. Technol. 123, 286–294 (2016).

Google Scholar

Zha, J. W., Zhang, B., Li, R. K. Y. & Dang, Z. M. High-performance strain sensors based on functionalized graphene nanoplates for damage monitoring. Compos Sci. Technol. 123, 32–38 (2016).

MATH Google Scholar

Chiechi, R. C., Weiss, E. A., Dickey, M. D. & Whitesides, G. M. Eutectic Gallium–Indium (EGaIn): A Moldable Liquid Metal for Electrical Characterization of Self-Assembled Monolayers. Angew. Chem. Int. Ed. 47, 142–144 (2008).

Google Scholar

Gul, O. et al. Sensitivity-controllable liquid-metal-based pressure sensor for wearable applications. ACS Appl. Electron. Mater. 3, 4027–4036 (2021).

MATH Google Scholar

Liu, Y. M. et al. Fully Elastic and High-Sensitivity Liquid Metal Sensor Based on Concave-Convex Structured Microchannel for Human Activity Monitoring and Object Recognition Sensor Array. ACS Appl. Electron. Mater. 5, 6157–6164 (2023).

MATH Google Scholar

Wang, Y. C., Jin, J., Lu, Y. T. & Mei, D. Q. 3D printing of liquid metal based tactile sensor for simultaneously sensing of temperature and forces. Int. J. Smart Nano Mater. 12, 269–285 (2021).

MATH Google Scholar

Pereira, R. D. & Cima, C. A. Thermal compensation method for piezoresistive pressure transducer. IEEE Trans. Instrum. Meas. 70, 1–7 (2021).

MATH Google Scholar

Zhou, G. W., Zhao, Y. L., Guo, F. F. & Xu, W. J. A smart high accuracy silicon piezoresistive pressure sensor temperature compensation system. Sensors 14, 12174–12190 (2014).

Google Scholar

He, W. N. et al. Polypyrrole/silver coaxial nanowire aero-sponges for temperature-independent stress sensing and stress-triggered joule heating. Acs Nano 9, 4244–4251 (2015).

MATH Google Scholar

Meng, X. Y. et al. Pressure‐Temperature Dual‐Parameter Flexible Sensors Based on Conformal Printing of Conducting Polymer PEDOT: PSS on Microstructured Substrate. Adv. Mater. Interfaces 10, 2201927 (2023).

Google Scholar

Yin, Y. M. et al. A flexible dual parameter sensor with hierarchical porous structure for fully decoupled pressure–temperature sensing. Chem. Eng. J. 430, 133158 (2022).

Google Scholar

Chen, Z. Y. et al. Decoupled Temperature-Pressure Sensing System for Deep Learning Assisted Human–Machine Interaction. Adv. Funct. Mater. https://doi.org/10.1002/adfm.202411688 (2024).

Li, M. et al. A flexible resistive strain gauge with reduced temperature effect via thermal expansion anisotropic composite substrate. Microsyst. Nanoeng. 10, 129 (2024).

MATH Google Scholar

Park, Y. L., Majidi, C., Kramer, R., Bérard, P. & Wood, R. J. Hyperelastic pressure sensing with a liquid-embedded elastomer. J. Micromech. Microeng. 20, 125029 (2010).

Google Scholar

Zhou, X. P., He, Y. & Zeng, J. Liquid metal antenna-based pressure sensor. Smart Mater. Struct. 28, 025019 (2019).

MATH Google Scholar

Nakadegawa, T., Ishizuka, H. & Miki, N. Three-axis scanning force sensor with liquid metal electrodes. Sens. Actuator A Phys. 264, 260–267 (2017).

Google Scholar

Deng, Y. G. & Liu, J. A liquid metal cooling system for the thermal management of high power LEDs. Int. Commun. Heat. Mass Transf. 37, 788–791 (2010).

MATH Google Scholar

Liu, R. Y. et al. Novel miniature valve-based piezoelectric liquid pump. Microsyst. Technol. https://doi.org/10.1007/s00542-024-05740-w (2024).

Jing, M. Y. et al. Porous AgNWs/Poly(vinylidene fluoride) Composite-Based Flexible Piezoresistive Sensor with High Sensitivity and Wide Pressure Ranges. ACS Appl. Mater. Interfaces 14, 55119–55129 (2022).

Google Scholar

Liu, C. et al. High-performance piezoresistive flexible pressure sensor based on wrinkled microstructures prepared from discarded vinyl records and ultra-thin, transparent polyaniline films for human health monitoring. J. Mater. Chem. C. 10, 13064–13073 (2022).

Google Scholar

Chen, S. J., Zhou, B. G. & Guo, X. J. Large Area One-Step Facile Processing of Microstructured Elastomeric Dielectric Film for High Sensitivity and Durable Sensing over Wide Pressure Range. ACS Appl. Mater. Interfaces 8, 20364–20370 (2016).

Google Scholar

Park, S. W., Das, P. S., Chhetry, A. & Park, J. Y. A Flexible Capacitive Pressure Sensor for Wearable Respiration Monitoring System. IEEE Sens. J. 17, 6558–6564 (2017).

MATH Google Scholar

Park, D. Y. et al. Self-Powered Real-Time Arterial Pulse Monitoring Using Ultrathin Epidermal Piezoelectric Sensors. Adv. Mater. 29, 1702308 (2017).

Google Scholar

Download references

The authors acknowledge the support of the Natural Science Foundation of Anhui Province (2108085QE226), Anhui Future Technology Research Institute Industry Guidance Fund Project (2023ccyd01), National Natural Science Foundation of China (No. 12472257), National Key Research and Development Program of China Stem Cell and Translational Research (2022YFB4600600).

School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu, 241000, China

Qing Wang, Zhou Zhou, Jizhang He, Wenjie Qian & Wei Shi

Guizhou Aerospace Linquan Motor Co. Ltd, Guiyang, 550014, China

Liang Zhuo

College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou, 310000, China

Chenlin Zhu

School of Aeronautics and Astronaut, Xiamen University, Xiamen, 361102, China

Daoheng Sun

You can also search for this author inPubMed Google Scholar

Z.Z. led the conception and interpretation of the experiment. W.Q. and H.J.Z. managed the experimental design and contributed to the manuscript preparation. S.W. and Q.W.J. assisted with the collection of experimental data. Z.L., Z.C.L. and S.D.H. provided guidance and support in both the experimental design and manuscript preparation. All authors engaged in discussing the results and offered comments on the paper.

Correspondence to Zhou Zhou.

The authors declare no competing interests.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

Wang, Q., Zhou, Z., He, J. et al. Multimodal response characteristics of convective liquid metal sensitive layers in flexible pressure sensor. Microsyst Nanoeng 11, 55 (2025). https://doi.org/10.1038/s41378-025-00915-5

Download citation

Received: 10 October 2024

Revised: 08 February 2025

Accepted: 04 March 2025

Published: 01 April 2025

DOI: https://doi.org/10.1038/s41378-025-00915-5

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative